Question: Solve for $x$ and $y$ using elimination. ${-4x+2y = -4}$ ${-3x-3y = -30}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $-4$ ${-12x+6y = -12}$ $12x+12y = 120$ Add the top and bottom equations together. $18y = 108$ $\dfrac{18y}{{18}} = \dfrac{108}{{18}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-4x+2y = -4}\thinspace$ to find $x$ ${-4x + 2}{(6)}{= -4}$ $-4x+12 = -4$ $-4x+12{-12} = -4{-12}$ $-4x = -16$ $\dfrac{-4x}{{-4}} = \dfrac{-16}{{-4}}$ ${x = 4}$ You can also plug ${y = 6}$ into $\thinspace {-3x-3y = -30}\thinspace$ and get the same answer for $x$ : ${-3x - 3}{(6)}{= -30}$ ${x = 4}$